Methods and forms of scientific cognition

The norms of a historically shaped culture arc reflected in the operations and modes of thought forged by the many ages of the work of reason. At present they have become universal tools of the­oretical cognition, taking shape as clear-cut rational devices, a sys­tem of principles and methods which, in their ensemble, can give an idea of the content wealth of the structure and modes of human thought today.

Analysis and synthesis. The movement from the sensuous-con­crete to the abstract and then to the concrete-in-thought includes above all such devices as analysis and synthesis. Analysis is the divi­sion of objects into their constituent parts or aspects in practical or the­oretical activity aimed at grasping some complex whole. When the particulars have been studied sufficiently well through analysis, the next stage in cognition comes, which is synthesis that impractical or mental combination of the elements, divided and studied analyti­cally, into a single whole. Analysis identifies primarily the specifics which distinguish the parts from one another, while synthesis reveals the essentially general which binds the parts into a single whole. Analysis which presupposes synthesis has as its central nucleus the identification of the essential. When that is done, the whole does not appear in the same light, either, as when reason first knows it — it now has much deeper content.

Abstraction and idealization. It is impossible to grasp an object in the entire fullness of its properties. Like a spotlight, human thought throws light at each given moment at a fragment of reality, while the rest sinks in gloom, as it were. At each of these moments we are aware of some one thing only—but this one thing has a great many properties and relations. We can cognize it only in the order of con­tinuity, by concentrating attention on some qualities and connec­tions and ignoring others.

Abstraction is a mental singling out of some object in isolation from its connections with other objects, of some property of an object in isolation from its other properties, of some relation of an object in isolation from the object itself. Abstraction is a method of mental simplification in which only one aspect of a given process is con­sidered.

The result of the process of abstraction are various concepts of objects (plant, animal, man), ideas on the separate properties of ob­jects and relations between them considered as particular "abstract objects" (whiteness, volume, length, heat capacity).

Idealization as a specific form of abstraction is an important de­vice of scientific cognition That is an abstrac­tion not to be found in nature. But abstractions are also images of the real: they are born of the generalization from experience. Ideal­ization is a process of forming concepts whose real prototypes may be pointed out only with a certain degree of approximation. The results of idealization are theoretical models in which the characteristics and aspects of the cognized object are not only abstracted from the actual empirical diversity but also appear as products of mental construction that are more clear-cut and fully pronounced than in reality. Examples of concepts resulting from idealization are the "point" (an object that has neither length nor height nor width), the "straight line", or the "circle". The introduction of idealized objects into the process of research permits the construction of abstract schemata of real processes, which are necessary for a deeper under­standing of the laws of their development.

Generalization and limitation. It would be impossible to cope with the hosts of impressions swamping us every hour, every minute and every second, if these impressions were not combined, gener­alized and recorded by means of language. Scientific generalization is not mere isolation and synthesis of similar features — it is penetration into the essence of a thing: the discovery of the identical in the diverse, of the general in the individual, of the law-governed in the accidental.

The mental transition from the more general to the less general is called limitation.

The abstract and the concrete. The concept of the concrete is used in two senses. First, it denotes a directly given, sensuously perceived and represented whole. Second, it denotes a system of scientific de­finitions identifying the essential connections and relations between things and events, identifying unity in diversity The sensuous-concrete is a pale reflection of phenomena, the concrete-in-thought is a much richer knowledge of the essence. The concrete is opposed to the abstract as one of the elements of cognition and is interpreted in correlation with the abstract. Ab­straction usually suggests to us something conceptual, in contrast to the sensuously observable.

Abstractions are a kind of replicas of integral objects. Human thought works with these replicas. Thought continually returns from separate abstractions to a restoration of concreteness on a new and higher basis. That is the concreteness of concepts, categories, and theories reflecting unity in diversity.

Herein lies the essence of the method of ascending from the ab­stract to the concrete. Abstraction realizes the principle of moving back to hit with greater certainty. By this method, the mind assimi­lates the concrete and constructs out of it, through linking up con­cepts, an integral scientific theory reproducing the objective hete­rogeneity of the object and the unity of its essential properties and relations

The principle of concreteness, considered in its inalienable links with the abstract, demands, that the facts of natural and social life be treated not with the aid of general formu­las and schemata but with due consideration for all the real condi­tions under which the object of cognition exists in order to identify the principal and most essential properties, connections, and tend­encies that determine its other aspects.

The historical and the logical. The historical is in the first place the process of the evolution of an object and also a method of its re­production in knowledge in the form in which it really took shape in time — with all the tribulations and zigzags and reverse movements, in the concrete and accidental forms of its manifestation. In other words, the historical method assumes the outlining of the history of an object as it really was, with due attention to the general and the individual or, at any rate, the typically individual.

The logical method reproduces the historical process only in its general form. It is aimed at the identification of the logic of the ob­ject's movement, of its general line of development — straightened out, as it were. The logical is a generalized reflection of the histori­cal, it reproduces reality in its law-governed development and ex­plains the necessity of that development. It is the historical freed from the principles of chronology, from its accidental and unique form. The logical method is grasped in the concept of the law of an object's development; that is to say, in applying it we inevitably ig­nore the accidental and individual nuances of a given event.

The real process of cognition, which en­deavours to see laws behind chance, relies on both these methods in their unity.

Analogy. Analogy is an objective relationship between objects that makes it possible to transfer the information obtained in the study of a given object onto another object resembling the former in terms of a definite set of features. Analogy, which links the unknown with the known, lies at the very heart of understanding facts. The new is consciously realized only through the images and concepts of the old and familiar. The first planes were constructed on the anal­ogy of the behaviour of other objects in flight, such as birds, kites and gliders.

Analogy is a verisimilar, feasible logical conclusion about the simi­larity of two objects in terms of some feature. As a method, analogy is most often used in the so-called theory of similarity, which is widely employed in modeling.

Modeling is the practical or theoretical operating an object in which the latter is replaced by some natural or arti­ficial analogue whose studying helps the researcher penetrate into the essence of that object. The objective basis of modelling is the principle of reflection, similarity, analogy, and the relative inde­pendence of form. A model is an objectified or mentally constructed system replacing the object of cognition. Any object re­producing the required features of the original may be a model. If a model has the same physical nature as the original, the reference is to physical modelling. When a phenomenon is described by the same system of equations as the modelling object, the modelling is termed mathematical.

Of course, modelling is always inevitably connected with a cer­tain simplification of the modelled object. But it plays a great heur­istic role, making it possible to study processes characteristic of the original in the absence of the original itself.

Formalization and mathematicization. Formalization is generali­zation of the forms of processes differing in content, abstraction of these forms from their content. Here form is regarded as a relatively independent object of study. It is often believed that formalization is connected with mathematics, mathematical logic, and cybernetics. That is not correct. It permeates all types of man's practical and theoretical activity. Historically, it emerged together with the ap­pearance of language. Our ordinary language expresses the weakest level of formalization. Formalization is at its extreme in mathematics and mathematical logic, which study the forms of reasoning in abstrac­tion from their content, maximally "denuding" thought, leaving only the framework of its structure intact

Today, the problem of interpretation, i.e. of establishment of the objective content of scientific knowledge, is becoming more and more acute. Abstraction becomes meaningless without concretization, while formalization has no meaning without interpretation. If formalization is the movement of thought from the content of an ob­ject to its abstract form, interpretation moves from the object's ab­stract form to its content. After it is constructed, a formal system again returns to its meaningful basis. Abstraction from content is temporary only.

What is mathematicization? It is the application of mathematical methods to scientific cognition. There was a time when these meth­ods were applied first and foremost to mechanics, physics, and as­tronomy, in short, to the natural sciences. Later they began to pene­trate into the social sciences, e.g., into sociological, economic and other studies. This was made possible by the achievements of cyber­netics.

Mathematics is needed by specialists in all fields not only to carry out calculations but also as a powerful heuristic device; it is also needed to introduce greater rigorousness and discipline into logical thinking. At the same time the limitations of formalization and mathematicization of scientific cognition are becoming increasingly clear. Modern science is developing on the path of a synthesis of formal and meaningful aspects of cognition on the basis of material­ism and dialectics.

Дата добавления: 2015-11-14